Siamese Neural Network for Label-Efficient Critical Phenomena Prediction in 3D Percolation Models
This work provides a label-efficient framework for materials science and complex network analysis, though it is incremental as it adapts existing Siamese networks to a specific 3D domain.
The paper tackled the problem of predicting critical phenomena in 3D percolation models with limited labeled data, achieving sub-1% error margins for thresholds and exponents using significantly fewer samples than traditional methods.
Percolation theory serves as a cornerstone for studying phase transitions and critical phenomena, with broad implications in statistical physics, materials science, and complex networks. However, most machine learning frameworks for percolation analysis have focused on two-dimensional systems, oversimplifying the spatial correlations and morphological complexity of real-world three-dimensional materials. To bridge this gap and improve label efficiency and scalability in 3D systems, we propose a Siamese Neural Network (SNN) that leverages features of the largest cluster as discriminative input. Our method achieves high predictive accuracy for both site and bond percolation thresholds and critical exponents in three dimensions, with sub-1% error margins using significantly fewer labeled samples than traditional approaches. This work establishes a robust and data-efficient framework for modeling high-dimensional critical phenomena, with potential applications in materials discovery and complex network analysis.